Majority Element Moore's Voting Algorithm in DSA Python - Execution Trace

Concept Flow - Majority Element Moore's Voting Algorithm

Initialize candidate and count

↓

For each element in array

↓

Is count zero?

Yes→Set candidate to current element

↓

Compare current element with candidate

↓

Increment count

↓

Decrement count

↓

After loop ends, candidate is majority element

↓

Return candidate

The algorithm scans the array once, keeping track of a candidate and a count. When count is zero, it picks a new candidate. It increments or decrements count based on matches. At the end, the candidate is the majority element.

Execution Sample

DSA Python

def majority_element(nums):
    count = 0
    candidate = None
    for num in nums:
        if count == 0:
            candidate = num
        count += (1 if num == candidate else -1)
    return candidate

This code finds the majority element in the list by updating candidate and count as it scans.

Execution Table

Step	Operation	Current Element	Candidate Before	Count Before	Candidate After	Count After	Visual State
1	Initialize	N/A	None	0	None	0	[]
2	Process element	3	None	0	3	1	[3] candidate=3, count=1
3	Process element	3	3	1	3	2	[3,3] candidate=3, count=2
4	Process element	4	3	2	3	1	[3,3,4] candidate=3, count=1
5	Process element	2	3	1	3	0	[3,3,4,2] candidate=3, count=0
6	Process element	4	3	0	4	1	[3,3,4,2,4] candidate=4, count=1
7	Process element	4	4	1	4	2	[3,3,4,2,4,4] candidate=4, count=2
8	Process element	4	4	2	4	3	[3,3,4,2,4,4,4] candidate=4, count=3
9	End	N/A	4	3	4	3	Final candidate=4, count=3

💡 All elements processed; candidate 4 is returned as majority element.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	After Step 7	After Step 8	Final
candidate	None	3	3	3	3	4	4	4	4
count	0	1	2	1	0	1	2	3	3

Key Moments - 3 Insights

Why do we reset the candidate when count reaches zero?

When count is zero (see Step 5), it means previous candidate's support is balanced out. We pick the current element as new candidate to find majority.

Why do we increment count only if current element equals candidate?

Incrementing count when element matches candidate (Steps 3,7,8) strengthens candidate's support; decrementing otherwise weakens it (Step 5). This balances votes.

How does the algorithm guarantee the candidate is the majority element?

Because majority element appears more than half times, it cannot be fully canceled out by others. After full scan (Step 9), candidate holds majority.

Visual Quiz - 3 Questions

Look at the execution_table at Step 5, what happens to count and candidate?

A Count resets to zero and candidate changes to 2

B Count decrements to zero but candidate stays 3

C Count increments and candidate changes to 2

D Count stays same and candidate changes to 4

💡 Hint

Check Step 5 row in execution_table: candidate before is 3, count before is 1, candidate after is 3, count after is 0

At which step does the candidate change from 3 to 4?

A Step 4

B Step 5

C Step 6

D Step 7

💡 Hint

Look at candidate after column in execution_table rows for steps 5 and 6

If the input array started with [4,4,4], how would count change after first three steps?

A Count would be 3 and candidate 4

B Count would be 1 and candidate 4

C Count would be 0 and candidate 4

D Count would be 3 and candidate 3

💡 Hint

Refer to variable_tracker and execution_table logic for increments when element equals candidate

Concept Snapshot

Majority Element Moore's Voting Algorithm:
- Initialize candidate=None, count=0
- For each element:
  - If count==0, set candidate=element
  - If element==candidate, count++ else count--
- Candidate at end is majority element
- Runs in O(n) time and O(1) space

Full Transcript

The Moore's Voting Algorithm finds the majority element by scanning the array once. It keeps a candidate and a count. When count is zero, it picks the current element as candidate. It increments count if the current element matches candidate, otherwise decrements count. This balances out votes. Because the majority element appears more than half the time, it cannot be fully canceled out. At the end, the candidate is the majority element. The example array [3,3,4,2,4,4,4] shows how candidate and count change step-by-step until candidate 4 remains with count 3.

Practice

1. What is the main purpose of Moore's Voting Algorithm in an array of numbers?

easy

A. To find the element that appears more than half the time

B. To sort the array in ascending order

C. To find the smallest element in the array

D. To count the total number of unique elements

Solution

1. Step 1: Understand the problem Moore's Voting Algorithm solves

   The algorithm is designed to find the majority element, which is the element that appears more than half the time in the array.

2. Step 2: Compare with other options

   Sorting, finding smallest element, or counting unique elements are not the goals of this algorithm.

3. Final Answer:

   To find the element that appears more than half the time -> Option A

4. Quick Check:

   Majority element = element with >50% frequency [OK]

Hint: Majority element appears more than half times [OK]

Common Mistakes:

• Confusing majority element with most frequent element
• Thinking it sorts the array
• Assuming it counts unique elements

2. Which of the following is the correct initialization step in Moore's Voting Algorithm in Python?

easy

A. count = 0; candidate = 0

B. count = 1; candidate = 0

C. count = None; candidate = 0

D. count = 0; candidate = None

Solution

1. Step 1: Recall initialization in Moore's Voting Algorithm

   We start with count = 0 and candidate = None to indicate no candidate chosen yet.

2. Step 2: Check other options for correctness

   Starting count at 1 or candidate at 0 without context is incorrect; None is used to indicate no candidate.

3. Final Answer:

   count = 0; candidate = None -> Option D

4. Quick Check:

   Initialize count=0 and candidate=None [OK]

Hint: Start count at 0 and candidate as None [OK]

Common Mistakes:

• Starting count at 1 instead of 0
• Assigning candidate to 0 prematurely
• Using None for count instead of candidate

3. What will be the output of the following code snippet?

def majority_element(nums):
    count = 0
    candidate = None
    for num in nums:
        if count == 0:
            candidate = num
        count += (1 if num == candidate else -1)
    return candidate

print(majority_element([2,2,1,1,1,2,2]))

medium

A. 2

B. 1

C. None

D. Error

Solution

1. Step 1: Trace the candidate and count updates

   Start with count=0, candidate=None. Iterate: 2 (count=0->1, candidate=2), 2 (count=2), 1 (count=1), 1 (count=0), 1 (count=1, candidate=1), 2 (count=0), 2 (count=1, candidate=2).

2. Step 2: Final candidate after iteration

   The candidate ends as 2 after the loop finishes.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Majority element in [2,2,1,1,1,2,2] is 2 [OK]

Hint: Track candidate changes when count hits zero [OK]

Common Mistakes:

• Not updating candidate when count is zero
• Confusing candidate with last element
• Assuming candidate is None if count resets

4. Identify the bug in this Moore's Voting Algorithm implementation:

def majority_element(nums):
    count = 0
    candidate = None
    for num in nums:
        if count == 0:
            candidate = num
        if num == candidate:
            count += 1
        else:
            count -= 1
    return candidate

print(majority_element([3,3,4]))

medium

A. Count increment/decrement logic is reversed

B. No bug, code works correctly

C. Candidate not updated when count is zero

D. Function does not handle empty list

Solution

1. Step 1: Analyze candidate update and count logic

   Candidate updates when count is zero. Count increments if current num equals candidate, else decrements.

2. Step 2: Test with input [3,3,4]

   Iteration: 3 (count=1, candidate=3), 3 (count=2), 4 (count=1). Returns candidate 3 correctly.

3. Final Answer:

   No bug, code works correctly -> Option B

4. Quick Check:

   Code correctly finds majority element [OK]

Hint: Check candidate update and count changes carefully [OK]

Common Mistakes:

• Thinking candidate is not updated when count is zero
• Confusing increment and decrement logic
• Ignoring empty list edge case

5. Given an array where no element appears more than half the time, what will Moore's Voting Algorithm return?
Example: [1,2,3,4]

hard

A. Error or exception

B. The element with highest frequency

C. None or incorrect candidate

D. The first element of the array

Solution

1. Step 1: Understand Moore's Voting Algorithm assumption

   The algorithm assumes a majority element exists (more than half the array). If none exists, it still returns a candidate but it may be incorrect.

2. Step 2: Apply to example [1,2,3,4]

   No element appears more than 2 times (half of 4). The algorithm returns a candidate but it is not a true majority.

3. Final Answer:

   None or incorrect candidate -> Option C

4. Quick Check:

   No majority means candidate may be wrong [OK]

Hint: Algorithm assumes majority exists; else candidate may be wrong [OK]

Common Mistakes:

• Assuming algorithm returns error if no majority
• Thinking it returns highest frequency element always
• Believing it returns first element by default